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This paper investigates the steady-state elastoplastic fields induced by a pressurized cylindrical cavity expanding dynamically in an anisotropic porous medium. For that task, we have developed a theoretical model which: (i) incorporates into the formalism developed by Cohen and Durban  the effect of plastic anisotropy using the constitutive framework developed by Benzerga and Besson  and (ii) uses the artificial viscosity approach developed by Lew et al.  to capture the shock waves that emerge at high cavity expansion velocities. We have shown that while the development of the shock waves is hardly affected by the material anisotropy, the directionality of the plastic properties does have an effect on the elastoplastic fields that evolve near the cavity. The importance of this effect is strongly dependent on the cavity expansion velocity, the initial porosity and the strain hardening of the material. In addition, the theoretical model has been used in conjunction with the Recht and Ipson  formulas to assess the ballistic performance of porous anisotropic targets against high velocity perforation.